C is the broken path line that goes from (1,1,2) to (2,0,-1) by
following a line parallel to the x axis from (1,1,2) to (2,1,2) then
parallel to the y axis from (2,1,2) to (2,0,2) then parallel to the z
axis from (2,0,2) to (2,0,-1). Find int_C [ f(x,y,z)*dx + g(x,y,z)*dy
+ h(x,y,z)*dz ].

A reader attempts to demonstrate infinity as concretely measurable in
an inversive geometric construction. Doctor Tom explains analyzes the
argument, weighing the pros and cons of the axioms of non-Euclidean
geometries, and going on to expose an apparent paradox.

Suppose you grab the end of a chain that weights 3 lb/ft and lift it
straight up off the floor at a constant speed of 2 ft/s: determine the
force as a function of height; how much work do you do in lifting the top
of the chain 4 feet?

A calculus teacher wonders how to prove a limit involving the factorial of a variable raised
to a power of the same unknown. Seeing an opportunity to prove a simple version of Stirling's Approximation, Doctor Vogler introduces it with integral calculus and the Squeeze Theorem.

I assumed from the graph that the function had a limit at x=0 of 0,
but since it involves sin(1/0) I can not prove this using the basic
trigonometric limits (sin x/x and (1-cos x)/x), L'Hopital's
rule, or by rearranging the equation. Can you help?